Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks

Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecular simulation, and polymer self-consistent field theory for networks to construct an equilibrium picture for how reversible crosslinks can toughen a polymer network without affecting its linear elasticity. Maximisation of polymer entropy drives the reversible crosslinks to bind preferentially near the permanent crosslinks in the network, leading to local molecular reinforcement without significant alteration of the network topology. In equilibrium conditions, permanent crosslinks share effectively the load with neighbouring reversible crosslinks, forming multi-functional crosslink points. The network is thereby globally toughened, while the linear elasticity is left largely unaltered. Practical guidelines are proposed to optimise this design in experiment, along with a discussion of key kinetic and timescale considerations

BVRIJK light curves and radial velocity curves for selected Magellanic Cloud Cepheids

We present high precision and well sampled BVRIJK light curves and radial velocity curves for a sample of five Cepheids in the SMC. In addition we present radial velocity curves for three Cepheids in the LMC. The low metallicity (Fe/H ~ -0.7) SMC stars have been selected for use in a Baade-Wesselink type analysis to constrain the metallicity effect on the Cepheid Period-Luminosity relation. The stars have periods of around 15 days so they are similar to the Cepheids observed by the Extragalactic Distance Scale Key Project on the Hubble Space Telescope. We show that the stars are representative of the SMC Cepheid population at that period and thus will provide a good sample for the proposed analysis. The actual Baade-Wesselink analysis are presented in a companion paper.Comment: Accepted for publication in A&A, 23 pages, 10 figures, data tables will be made available electronically from the CD

Generalized Geologic Map for Land-Use Planning: Clay County, Kentucky

This map is not intended to be used for selecting individual sites. Its purpose is to inform land-use planners, government officials, and the public in a general way about geologic bedrock conditions that affect the selection of sites for various purposes. The properties of thick soils may supercede those of the underlying bedrock and should be considered on a site-to-site basis. At any site, it is important to understand the characteristics of both the soils and the underlying rock

Finite-time Lyapunov exponents of deep neural networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.Comment: 6 pages, 4 figure

A New Calibration Of Galactic Cepheid Period-Luminosity Relations From B To K Bands, And A Comparison To LMC Relations

Context. The universality of the Cepheid period-luminosity (PL) relations has been under discussion since metallicity effects were assumed to play a role in the value of the intercept and, more recently, of the slope of these relations. Aims. The goal of the present study is to calibrate the Galactic PL relations in various photometric bands (from B to K) and to compare the results to the well-established PL relations in the LMC. Methods. We use a set of 59 calibrating stars, the distances of which are measured using five different distance indicators: Hubble Space Telescope and revised Hipparcos parallaxes, infrared surface brightness and interferometric Baade-Wesselink parallaxes, and classical Zero-Age-Main-Sequence-fitting parallaxes for Cepheids belonging to open clusters or OB stars associations. A detailed discussion of absorption corrections and projection factor to be used is given. Results. We find no significant difference in the slopes of the PL relations between LMC and our Galaxy. Conclusions. We conclude that the Cepheid PL relations have universal slopes in all photometric bands, not depending on the galaxy under study (at least for LMC and Milky Way). The possible zero-point variation with metal content is not discussed in the present work, but an upper limit of 18.50 for the LMC distance modulus can be deduced from our data.McDonald Observator

The Araucaria Project. OGLE-LMC-CEP-1718: An exotic eclipsing binary system composed of two classical overtone Cepheids in a 413-day orbit

We have obtained extensive high-quality spectroscopic observations of the OGLE-LMC-CEP-1718 eclipsing binary system in the Large Magellanic Cloud which Soszynski et al. (2008) had identified as a candidate system for containing two classical Cepheids in orbit. Our spectroscopic data clearly demonstrate binary motion of the Cepheids in a 413-day eccentric orbit, rendering this eclipsing binary system the first ever known to consist of two classical Cepheid variables. After disentangling the four different radial velocity variations in the system we present the orbital solution and the individual pulsational radial velocity curves of the Cepheids. We show that both Cepheids are extremely likely to be first overtone pulsators and determine their respective dynamical masses, which turn out to be equal to within 1.5 %. Since the secondary eclipse is not observed in the orbital light curve we cannot derive the individual radii of the Cepheids, but the sum of their radii derived from the photometry is consistent with overtone pulsation for both variables. The existence of two equal-mass Cepheids in a binary system having different pulsation periods (1.96 and 2.48 days, respectively) may pose an interesting challenge to stellar evolution and pulsation theories, and a more detailed study of this system using additional datasets should yield deeper insight about the physics of stellar evolution of Cepheid variables. Future analysis of the system using additional near-infrared photometry might also lead to a better understanding of the systematic uncertainties in current Baade-Wesselink techniques of distance determinations to Cepheid variables.Comment: accepted to be published in Ap

Atmospheric parameters of Cepheids from flux ratios with ATHOS: I. The temperature scale

Context: The effective temperature is a key parameter governing the properties of a star. For stellar chemistry, it has the strongest impact on the accuracy of the abundances derived. Since Cepheids are pulsating stars, determining their effective temperature is more complicated that in the case of non-variable stars. Aims: We want to provide a new temperature scale for classical Cepheids, with a high precision and full control of the systematics. Methods: Using a data-driven machine learning technique employing observed spectra, and taking great care to accurately phase single-epoch observations, we have tied flux ratios to (label) temperatures derived using the infrared surface brightness method. Results: We identified 143 flux ratios that allow us to determine the effective temperature with a precision of a few K and an accuracy better than 150 K, which is in line with the most accurate temperature measures available to date. The method does not require a normalization of the input spectra and provides homogeneous temperatures for low- and high-resolution spectra, even at the lowest signal-to-noise ratios. Due to the lack of a dataset of sufficient sample size for Small Magellanic Cloud Cepheids, the temperature scale does not extend to Cepheids with [Fe/H] < -0.6 dex but nevertheless provides an exquisite, homogeneous means of characterizing Galactic and Large Magellanic Cloud Cepheids. Conclusions: The temperature scale will be extremely useful in the context of spectroscopic surveys for Milky Way archaeology with the WEAVE and 4MOST spectrographs. It paves the way for highly accurate and precise metallicity estimates, which will allow us to assess the possible metallicity dependence of Cepheids' period-luminosity relations and, in turn, to improve our measurement of the Hubble constant H0.Comment: 16 pages, 13 figures, accepted in A&